Looks good enough. On the resistors though, you will soon find out that you want different values, especially when you're dealing with LEDs. More than just the '82's like that kit offers. Also, 10Ks are handy to have a bunch of.

Some others, no, they would need wire leads soldered on. None of them I know can't take 5V 40 mA.

When you see leads on 5mm centers, 1mm is very close to .04" where breadboard holes are .1" apart.I had more trouble with he width of the legs but even without squeezing the legs in a crimp tool, they fit.

They have some with pins on .1" spacing but more expensive and the ones 10/$1 don't all just fit.

I've got old computers at my parents place. I've definitely used the powersupplies before for +12v (jumper the green mobo wire to ground). Is the +5v rail suitable to power the Arduino unit?

yes the 5v+ rail is regulated at 5 volts which is safe, the 3.3v rail is unregulated so stick to the 5v rail, in my setup I have a arduino clone teensy from pjrc. running some 12 volt motors. all off the same power supply. in my conversion I added a few 5 amp fuses to prevent being slapped around with all 20 amps for long periods of time.